Global estimates for non-uniformly nonlinear elliptic equations in a convex domain

In this paper we obtain the following global a priori Calderón–Zygmund estimates in a convex domain Ω|f|p1+|f|p2∈Lγ(Ω)⇒|∇u|p1+|∇u|p2∈Lγ(Ω)for anyγ≥1 of weak solutions for a class of non-uniformly nonlinear elliptic equations with vanishing Dirichlet data∑i=12div((Ai∇u⋅∇u)pi−22Ai∇u)=∑i=12div(|f|pi−2f), where 1